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(x-5)(5x-12)=25
We move all terms to the left:
(x-5)(5x-12)-(25)=0
We multiply parentheses ..
(+5x^2-12x-25x+60)-25=0
We get rid of parentheses
5x^2-12x-25x+60-25=0
We add all the numbers together, and all the variables
5x^2-37x+35=0
a = 5; b = -37; c = +35;
Δ = b2-4ac
Δ = -372-4·5·35
Δ = 669
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{669}}{2*5}=\frac{37-\sqrt{669}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{669}}{2*5}=\frac{37+\sqrt{669}}{10} $
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